So the steps will be akin to moving WordPress.... that is essentially what you are doing.
Even if you just rename the directory, to WP, it is being moved to a new subdirectory
As for your media concerns, this plugin seems to work well
http://wordpress.org/extend/plugins/search-and-replace/
Your media links are hardcoded in the database to the existing URL. So the plugin ca search and replace in the database any instances of your old url (I've never used it, but it seems to work for a lot of folks)